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Journal articles on the topic 'Boussinesq-Type'

Author: Grafiati

Published: 23 November 2024

Last updated: 31 July 2025

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1

McCann, Maile, Patrick Lynett, and Behzad Ebrahimi. "FREQUENCY DISPERSION IN DEPTH-INTEGRATED MODELS THROUGH MACHINE LEARNING SURROGATES." Coastal Engineering Proceedings, no. 37 (September 1, 2023): 54. http://dx.doi.org/10.9753/icce.v37.waves.54.

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Boussinesq- type wave models have the accuracy to resolve wave propagation in coastal zones, having the ability to capture nearshore dynamics that include both nonlinear and dispersive effects for relatively short waves. The accuracy of Boussinesq type models over their counterparts which utilize the non- linear shallow water (NLSW) equations provides a clear advantage in studying nearshore processes. However, the computational expense of finding the Boussinesq solution over the NLSW solution hinders fast and/ or real time simulation using Boussinesq type models.

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2

Yuldashev, Tursun. "Mixed Boussinesq-Type Differential Equation." Vestnik Volgogradskogo gosudarstvennogo universiteta. Serija 1. Mathematica. Physica, no. 2 (June 2016): 13–26. http://dx.doi.org/10.15688/jvolsu1.2016.2.2.

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3

De BRYE, Sébastien, Rodolfo Silva, and Edgar Mendoza. "BOUSSINESQ TYPE MODELLING OF STORM SURGES." Coastal Engineering Proceedings 1, no. 33 (2012): 15. http://dx.doi.org/10.9753/icce.v33.posters.15.

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To get a better understanding of transient stages of storm surges, this work examines the response of a Boussinesq type model to a moving low pressure system forcing, discussing results through numerical simulations in one horizontal dimension.

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4

Engelbrecht, Jüri, Tanel Peets, and Kert Tamm. "Solitons modelled by Boussinesq-type equations." Mechanics Research Communications 93 (October 2018): 62–65. http://dx.doi.org/10.1016/j.mechrescom.2017.05.008.

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5

Meletlidou, Efi, Joël Pouget, Gérard Maugin, and Elias Aifantis. "Invariant relations in Boussinesq-type equations." Chaos, Solitons & Fractals 22, no. 3 (2004): 613–25. http://dx.doi.org/10.1016/j.chaos.2004.02.007.

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6

Schäffer, Hemming A., and Per A. Madsen. "Further enhancements of Boussinesq-type equations." Coastal Engineering 26, no. 1-2 (1995): 1–14. http://dx.doi.org/10.1016/0378-3839(95)00017-2.

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7

Murawski, K. "Instabilities of generalized Boussinesq-type waves." Wave Motion 10, no. 2 (1988): 161–69. http://dx.doi.org/10.1016/0165-2125(88)90041-8.

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8

Boukarou, Aissa, Safa M. Mirgani, Khaled Zennir, Keltoum Bouhali, and Sultan S. Alodhaibi. "White-Noise-Driven KdV-Type Boussinesq System." Mathematics 13, no. 11 (2025): 1758. https://doi.org/10.3390/math13111758.

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The white-noise-driven KdV-type Boussinesq system is a class of stochastic partial differential equations (SPDEs) that describe nonlinear wave propagation under the influence of random noise—specifically white noise—and generalize features from both the Korteweg–de Vries (KdV) and Boussinesq equations. We consider a Cauchy problem for two stochastic systems based on the KdV-type Boussinesq equations. For these systems, we determine sufficient conditions to ensure that this problem is locally and globally well posed for initial data in Sobolev spaces by the linear and bilinear estimates and the

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9

Luo, Dejun. "Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system." Nonlinearity 34, no. 12 (2021): 8311–30. http://dx.doi.org/10.1088/1361-6544/ac3145.

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Abstract The inviscid 2D Boussinesq system with thermal diffusivity and multiplicative noise of transport type is studied in the L 2-setting. It is shown that, under a suitable scaling of the noise, weak solutions to the stochastic 2D Boussinesq equations converge weakly to the unique solution of the deterministic viscous Boussinesq system. Consequently, the transport noise asymptotically regularises the inviscid 2D Boussinesq system and enhances dissipation in the limit.

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10

Song, Changming, Jina Li, and Ran Gao. "Nonexistence of Global Solutions to the Initial Boundary Value Problem for the Singularly Perturbed Sixth-Order Boussinesq-Type Equation." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/928148.

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We are concerned with the singularly perturbed Boussinesq-type equation including the singularly perturbed sixth-order Boussinesq equation, which describes the bidirectional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for bond number (surface tension parameter) less than but very close to 1/3. The nonexistence of global solution to the initial boundary value problem for the singularly perturbed Boussinesq-type equation is discussed and two examples are given.

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11

Taskesen, Hatice, Necat Polat, and Abdulkadir Ertaş. "On Global Solutions for the Cauchy Problem of a Boussinesq-Type Equation." Abstract and Applied Analysis 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/535031.

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We will give conditions which will guarantee the existence of global weak solutions of the Boussinesq-type equation with power-type nonlinearity and supercritical initial energy. By defining new functionals and using potential well method, we readdressed the initial value problem of the Boussinesq-type equation for the supercritical initial energy case.

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12

WEAAM, ALHEJAILI, WAZWAZ ABDUL-MAJID, and EL-TANTAWY S. A. "On the multiple soliton and lump solutions to the (3+1)-dimensional Painlevé integrable Boussinesq-type and KP-type equations." Romanian Reports in Physics 76, no. 4 (2024): 115. http://dx.doi.org/10.59277/romrepphys.2024.76.115.

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This study aims to construct and investigate a novel (3+1)-dimensional model that combines both the Boussinesq-type and the Kadomtsev-Petviashvili (KP) equations, which is called a (3+1)-dimensional Boussinesq-KP-type (B-KP-type) equation. We demonstrate that the combined model does not exhibit Painleve integrability. However, it does provide two separate integrable equations: one of the (3+1)-dimensional Boussinesq-type equation and the other of the (3+1)-dimensional KP-type equation. The simplified Hirota’s direct approach can formally admit multiple soliton solutions for each integrable mod

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13

IVANOV, E., S. KRIVONOS, and R. P. MALIK. "BOUSSINESQ-TYPE EQUATIONS FROM NONLINEAR REALIZATIONS OF W3." International Journal of Modern Physics A 08, no. 18 (1993): 3199–222. http://dx.doi.org/10.1142/s0217751x93001284.

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We construct new coset realizations of infinite-dimensional linear [Formula: see text] symmetry associated with Zamolodchikov's W3 algebra which are different from the previously explored sl3 Toda realizations of [Formula: see text]. We deduce the Boussinesq and modified Boussinesq equations as constraints on the geometry of the corresponding coset manifolds. The main characteristic features of these realizations are: (i) among the coset parameters there are space and time coordinates x and t which enter the Boussinesq equations; all other coset parameters are regarded as fields depending on t

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14

Yang, Zonghang, and Benny Y. C. Hon. "An Improved Modified Extended tanh-Function Method." Zeitschrift für Naturforschung A 61, no. 3-4 (2006): 103–15. http://dx.doi.org/10.1515/zna-2006-3-401.

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In this paper we further improve the modified extended tanh-function method to obtain new exact solutions for nonlinear partial differential equations. Numerical applications of the proposed method are verified by solving the improved Boussinesq equation and the system of variant Boussinesq equations. The new exact solutions for these equations include Jacobi elliptic doubly periodic type,Weierstrass elliptic doubly periodic type, triangular type and solitary wave solutions

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15

Kennedy, Andrew B., James T. Kirby, Qin Chen, and Robert A. Dalrymple. "Boussinesq-type equations with improved nonlinear performance." Wave Motion 33, no. 3 (2001): 225–43. http://dx.doi.org/10.1016/s0165-2125(00)00071-8.

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16

Zou, Z. L., P. C. Hu, K. Z. Fang, and Z. B. Liu. "Boussinesq-type equations for wave–current interaction." Wave Motion 50, no. 4 (2013): 655–75. http://dx.doi.org/10.1016/j.wavemoti.2013.01.001.

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17

Klonaris, Georgios Th, and Constantine D. Memos. "Compound Boussinesq-type modelling over porous beds." Applied Ocean Research 105 (December 2020): 102422. http://dx.doi.org/10.1016/j.apor.2020.102422.

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18

Passerini, Arianna, and Gudrun Thäter. "Boussinesq-type approximation for second-grade fluids." International Journal of Non-Linear Mechanics 40, no. 6 (2005): 821–31. http://dx.doi.org/10.1016/j.ijnonlinmec.2004.07.019.

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19

Rosenau, P., and J. L. Schwarzmeier. "On similarity solutions of Boussinesq-type equations." Physics Letters A 115, no. 3 (1986): 75–77. http://dx.doi.org/10.1016/0375-9601(86)90026-5.

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20

Kazolea, M., and M. Ricchiuto. "On wave breaking for Boussinesq-type models." Ocean Modelling 123 (March 2018): 16–39. http://dx.doi.org/10.1016/j.ocemod.2018.01.003.

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21

FENG, WEI, SONG-LIN ZHAO, and DA-JUN ZHANG. "EXACT SOLUTIONS TO LATTICE BOUSSINESQ-TYPE EQUATIONS." Journal of Nonlinear Mathematical Physics 19, no. 04 (2012): 1250031. http://dx.doi.org/10.1142/s1402925112500313.

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In this paper several kinds of exact solutions to lattice Boussinesq-type equations are constructed by means of generalized Cauchy matrix approach, including soliton solutions and mixed solutions. The introduction of the general condition equation set yields that all solutions contain two kinds of plane-wave factors.

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22

Memos, Constantine D., Georgios Th Klonaris, and Michalis K. Chondros. "On Higher-Order Boussinesq-Type Wave Models." Journal of Waterway, Port, Coastal, and Ocean Engineering 142, no. 1 (2016): 04015011. http://dx.doi.org/10.1061/(asce)ww.1943-5460.0000317.

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23

Fokas, A. S., and B. Pelloni. "Boundary Value Problems for Boussinesq Type Systems." Mathematical Physics, Analysis and Geometry 8, no. 1 (2005): 59–96. http://dx.doi.org/10.1007/s11040-004-1650-6.

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24

Pavlov, M. V. "The Boussinesq equation and Miura-type transformations." Journal of Mathematical Sciences 136, no. 6 (2006): 4478–83. http://dx.doi.org/10.1007/s10958-006-0239-y.

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25

Hwang, Sooncheol, Sangyoung Son, and Patrick J. Lynett. "A GPU-ACCELERATED MODELING OF SCALAR TRANSPORT BASED ON BOUSSINESQ-TYPE EQUATIONS." Coastal Engineering Proceedings, no. 36v (December 28, 2020): 11. http://dx.doi.org/10.9753/icce.v36v.waves.11.

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This paper describes a two-dimensional scalar transport model solving advection-diffusion equation based on GPU-accelerated Boussinesq model called Celeris. Celeris is the firstly-developed Boussinesq-type model that is equipped with an interactive system between user and computing unit. Celeris provides greatly advantageous user-interface that one can change not only water level, topography but also model parameters while the simulation is running. In this study, an advection-diffusion equation for scalar transport was coupled with extended Boussinesq equations to simulate scalar transport in

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26

Shi, Jincheng, and Yan Liu. "Continuous Dependence for the Boussinesq Equations under Reaction Boundary Conditions in R2." Mathematics 10, no. 6 (2022): 991. http://dx.doi.org/10.3390/math10060991.

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In this paper, we studied the continuous dependence result for the Boussinesq equations. We considered the case where Ω was a bounded domain in R2. Temperatures T and C satisfied reaction boundary conditions. A first-order inequality for the differences of energy could be derived. An integration of this inequality produced a continuous dependence result. The result told us that the continuous dependence type stability was also valid for the Boussinesq coefficient λ of the Boussinesq equations with reaction boundary conditions.

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27

Castro, Ángel, Diego Córdoba, and Daniel Lear. "On the asymptotic stability of stratified solutions for the 2D Boussinesq equations with a velocity damping term." Mathematical Models and Methods in Applied Sciences 29, no. 07 (2019): 1227–77. http://dx.doi.org/10.1142/s0218202519500210.

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We consider the 2D Boussinesq equations with a velocity damping term in a strip domain, with impermeable walls. In this physical scenario, where the Boussinesq approximation is accurate when density or temperature variations are small, our main result is the asymptotic stability for a specific type of perturbations of a stratified solution.

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28

PRUŠA, VÍT, and K. R. RAJAGOPAL. "ON MODELS FOR VISCOELASTIC MATERIALS THAT ARE MECHANICALLY INCOMPRESSIBLE AND THERMALLY COMPRESSIBLE OR EXPANSIBLE AND THEIR OBERBECK–BOUSSINESQ TYPE APPROXIMATIONS." Mathematical Models and Methods in Applied Sciences 23, no. 10 (2013): 1761–94. http://dx.doi.org/10.1142/s0218202513500516.

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Viscoelastic fluid like materials that are mechanically incompressible but are compressible or expansible with respect to thermal stimuli are of interest in various applications ranging from geophysics and polymer processing to glass manufacturing. Here we develop a thermodynamical framework for the modeling of such materials. First we illustrate the basic ideas in the simpler case of a viscous fluid, and after that we use the notion of natural configuration and the concept of the maximization of the entropy production, and we develop a model for a Maxwell type viscoelastic fluid that is mecha

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29

YANG, XIAO-JUN, J. A. TENREIRO MACHADO, and DUMITRU BALEANU. "EXACT TRAVELING-WAVE SOLUTION FOR LOCAL FRACTIONAL BOUSSINESQ EQUATION IN FRACTAL DOMAIN." Fractals 25, no. 04 (2017): 1740006. http://dx.doi.org/10.1142/s0218348x17400060.

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The new Boussinesq-type model in a fractal domain is derived based on the formulation of the local fractional derivative. The novel traveling wave transform of the non-differentiable type is adopted to convert the local fractional Boussinesq equation into a nonlinear local fractional ODE. The exact traveling wave solution is also obtained with aid of the non-differentiable graph. The proposed method, involving the fractal special functions, is efficient for finding the exact solutions of the nonlinear PDEs in fractal domains.

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30

Yang, Zhijian, Na Feng, and Yanan Li. "Robust attractors for a Kirchhoff-Boussinesq type equation." Evolution Equations & Control Theory 9, no. 2 (2020): 469–88. http://dx.doi.org/10.3934/eect.2020020.

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31

MORI, Tomohiro, and Takenori SHIMOZONO. "LEVEE OVERFLOW SIMULATION BY MODIFIED BOUSSINESQ-TYPE EQUATIONS." Journal of Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering) 73, no. 2 (2017): I_13—I_18. http://dx.doi.org/10.2208/kaigan.73.i_13.

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32

Chondros, Michalis K., Iason G. Koutsourelakis, and Constantine D. Memos. "A Boussinesq-type model incorporating random wave-breaking." Journal of Hydraulic Research 49, no. 4 (2011): 529–38. http://dx.doi.org/10.1080/00221686.2011.571817.

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33

Otta, Ashwini K., and Hemming A. Schäffer. "Finite-amplitude analysis of some Boussinesq-type equations." Coastal Engineering 36, no. 4 (1999): 323–41. http://dx.doi.org/10.1016/s0378-3839(99)00012-5.

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34

Yang, Zhijian, and Xia Wang. "Blowup of solutions for improved Boussinesq type equation." Journal of Mathematical Analysis and Applications 278, no. 2 (2003): 335–53. http://dx.doi.org/10.1016/s0022-247x(02)00516-4.

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35

de Brye, Sébastien, Rodolfo Silva, and Adrián Pedrozo-Acuña. "An LDG numerical approach for Boussinesq type modelling." Ocean Engineering 68 (August 2013): 77–87. http://dx.doi.org/10.1016/j.oceaneng.2013.04.017.

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36

Steinmoeller, D. T., M. Stastna, and K. G. Lamb. "Fourier pseudospectral methods for 2D Boussinesq-type equations." Ocean Modelling 52-53 (August 2012): 76–89. http://dx.doi.org/10.1016/j.ocemod.2012.05.003.

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37

Li, Y. S., and J. M. Zhan. "Boussinesq-Type Model with Boundary-Fitted Coordinate System." Journal of Waterway, Port, Coastal, and Ocean Engineering 127, no. 3 (2001): 152–60. http://dx.doi.org/10.1061/(asce)0733-950x(2001)127:3(152).

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38

Grajales, Juan Carlos Muñoz, and André Nachbin. "Improved Boussinesq-type equations for highly variable depth." IMA Journal of Applied Mathematics 71, no. 4 (2006): 600–633. http://dx.doi.org/10.1093/imamat/hxl008.

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39

Simarro, Gonzalo, Alejandro Orfila, and Alvaro Galan. "Linear shoaling in Boussinesq-type wave propagation models." Coastal Engineering 80 (October 2013): 100–106. http://dx.doi.org/10.1016/j.coastaleng.2013.05.009.

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40

Bonar, Paul A. J., Colm J. Fitzgerald, Zhiliang Lin, Ton S. van den Bremer, Thomas A. A. Adcock, and Alistair G. L. Borthwick. "Anomalous wave statistics following sudden depth transitions: application of an alternative Boussinesq-type formulation." Journal of Ocean Engineering and Marine Energy 7, no. 2 (2021): 145–55. http://dx.doi.org/10.1007/s40722-021-00192-0.

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AbstractRecent studies of water waves propagating over sloping seabeds have shown that sudden transitions from deeper to shallower depths can produce significant increases in the skewness and kurtosis of the free surface elevation and hence in the probability of rogue wave occurrence. Gramstad et al. (Phys. Fluids 25 (12): 122103, 2013) have shown that the key physics underlying these increases can be captured by a weakly dispersive and weakly nonlinear Boussinesq-type model. In the present paper, a numerical model based on an alternative Boussinesq-type formulation is used to repeat these ear

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41

Belmiloudi, Aziz. "Robin-type boundary control problems for the nonlinear Boussinesq type equations." Journal of Mathematical Analysis and Applications 273, no. 2 (2002): 428–56. http://dx.doi.org/10.1016/s0022-247x(02)00252-4.

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42

Xing, Zhaojun. "Single-component regularity criterion and inviscid limit for axially symmetric MHD-Boussinesq systems." Electronic Journal of Differential Equations 2025, no. 01-?? (2025): 68. https://doi.org/10.58997/ejde.2025.68.

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In this article, we give a critical BKM-type blow-up criterion that only involves the horizontal swirl component of the velocity for inviscid axially symmetric MHD-Boussinesq systems. We consider the inviscid limit for viscous MHD-Boussinesq systems, and the convergence rate as the viscosity coefficient tending to zero. For more information see https://ejde.math.txstate.edu/Volumes/2025/68/abstr.html

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43

Gao Liang, Xu Wei, Tang Ya-Ning, and Shen Jian-Wei. "New explicit exact solutions of one type of generalized Boussinesq equations and the Boussinesq-Burgers equation." Acta Physica Sinica 56, no. 4 (2007): 1860. http://dx.doi.org/10.7498/aps.56.1860.

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44

Wu, Qiang, Lin Hu, and Guili Liu. "An Osgood Type Regularity Criterion for the 3D Boussinesq Equations." Scientific World Journal 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/563084.

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45

Su, Yan. "Numerical Researches of Rectangular Barge in Variable Bathymetry Based on Boussinesq-Step Method." Advances in Civil Engineering 2022 (August 18, 2022): 1–9. http://dx.doi.org/10.1155/2022/2209394.

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Wave responses of the rectangular barge in variable bathymetry are investigated by combining the Boussinesq-type equations and the step method. The highly accurate Boussinesq-type equations in terms of velocity potential are adopted for simulating the evolution of waves along the inclined beach. Hydrodynamic coefficients of a rectangular barge floating on the inclined bottom are calculated by the step method in the frequency domain. Based on the impulse response function method, the motions of the barge can be predicted in the time domain. The Haskind relation is used to reform the wave exciti

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46

Zhang, Wei. "A priori estimates for the free boundary problem of incompressible inviscid Boussinesq and MHD-Boussinesq equations without heat diffusion." AIMS Mathematics 8, no. 3 (2022): 6074–94. http://dx.doi.org/10.3934/math.2023307.

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<abstract><p>For all physical spatial dimensions $ n = 2 $ and $ 3 $, we establish a priori estimates of Sobolev norms for free boundary problem of inviscid Boussinesq and MHD-Boussinesq equations without heat diffusion under the Taylor-type sign condition on the initial free boundary. It is different from MHD equations because the energy of the system is not conserved.</p></abstract>

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47

Capistrano–Filho, Roberto A., Ademir F. Pazoto, and Lionel Rosier. "Control of a Boussinesq system of KdV–KdV type on a bounded interval." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 58. http://dx.doi.org/10.1051/cocv/2018036.

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We consider a Boussinesq system of KdV–KdV type introduced by J.L. Bona, M. Chen and J.-C. Saut as a model for the motion of small amplitude long waves on the surface of an ideal fluid. This system of two equations can describe the propagation of waves in both directions, while the single KdV equation is limited to unidirectional waves. We are concerned here with the exact controllability of the Boussinesq system by using some boundary controls. By reducing the controllability problem to a spectral problem which is solved by using the Paley–Wiener method introduced by the third author for KdV,

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48

Guo, Xiu-Rong, Gui-Lei Chen, Mei Guo, and Zheng-Tao Liu. "A periodic solution for the local fractional Boussinesq equation on cantor sets." Thermal Science 23, no. 6 Part B (2019): 3719–23. http://dx.doi.org/10.2298/tsci180822255g.

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In this paper, the periodic solution for the local fractional Boussinesq equation can be obtained in the sense of the local fractional derivative. It is given by applying direct integration with symmetry condition. Meanwhile, the periodic solution of the non-differentiable type with generalized functions defined on Cantor sets is analyzed. As a result, we have a new point to look the local fractional Boussinesq equation through the local fractional derivative theory.

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49

sci, Joao Guilherme Caldas Steinstraesser. "A Domain Decomposition Method for Linearized Boussinesq-Type Equations." Journal of Mathematical Study 52, no. 3 (2019): 320–40. http://dx.doi.org/10.4208/jms.v52n3.19.06.

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50

Hutahaean, Syawaluddin. "Boussinesq-type Equation Formulated using the Weighted Taylor Series." International Journal of Advanced Engineering Research and Science 8, no. 12 (2021): 259–65. http://dx.doi.org/10.22161/ijaers.812.25.

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